Magnetic resonance imaging (MRI) is a well-known way of imaging the human body or other subject. In MRI, a strong magnetic field is applied to a subject causing precession of the protons in water molecules in the subject. Contrast between different tissues may be achieved by measuring the relaxation time of the precessing protons (T1 weighting) or by measuring the time that it takes the precessing protons to lose coherence (T2 weighting).
Diffusion-weighted imaging (DWI) is an MRI technique that is used to measure the diffusion of water in tissue. A DWI sequence uses two motion-probing gradient (MPG) pulses to selectively attenuate the signal of diffused fluid. The first MPG pulse is applied, resulting in dephasing of the proton spins. After a time interval, the second MPG pulse is applied. The second MPG pulse has the same magnitude as the first MPG pulse and may have the same direction or opposite direction to the first MPG pulse depending on the sequence. In a gradient-echo sequence, the direction of the second MPG pulse is opposite to the first MPG pulse. In a spin-echo sequence, the direction of the second MPG pulse is the same as the direction of the first MPG pulse.
If the water molecules have not moved during the interval between the first MPG pulse and the second MPG pulse, the second pulse compensates for the dephasing that resulted from the first pulse. However, if the molecules have diffused, then the dephasing is not fully compensated in protons that have moved. Water that has been diffused during the interval between pulses appears darker in the scan than water that has not been diffused. The attenuation is proportional to the amount of diffusion.
The degree of diffusion weighting achieved by the MPG pulses may be summarized in a single value, known as the b-value. The b-value depends on the acquisition parameters for the scan. Acquisition parameters include the gradient amplitude, the time at which the gradient is applied, and the time interval between the two MPG pulses. The higher the b-value, the greater the diffusion weighting.
An image resulting from a DWI scan will be diffusion-weighted, but may also exhibit T1 or T2 weighting. In order to separate out the effect of diffusion from the effect of T1 or T2 weighting, the DWI scan image may be compared with a reference image of the same subject for which b=0.
Most DWI sequences are based on echo-planar imaging (EPI). Echo-planar imaging is a technique that is used to produce rapid MRI images. Each radio-frequency excitation used in the MRI scan is followed by a train of gradient echoes. A scan image taken using EPI imaging with the addition of MPG pulses (a scan where b>0), may be compared with a scan image of the same subject that is taken using EPI imaging without MPG pulses. The image obtained from the scan with MPG pulses may be referred to as a DWI image. The image obtained from the scan without MPG pulses (a scan where b=0) may be referred to as an EPI image. The DWI image and EPI image may be compared to separate out the effect of diffusion.
To assess diffusion using a DWI image, the DWI image (b>0) and its corresponding EPI reference image (b=0) must be taken as part of the same series of scans. The series of scans may also include other MRI scan types, for example scans producing T2-weighted (T2W) images.
EPI and DWI images are subject to distortions, which may in some cases be substantial. Representative distortions are illustrated in FIGS. 1(a) and 1(b). T2W images are acquired using spin echo sequences and do not experience distortion of the types described below (EPI and MPG distortion).
Echo-planar imaging distortion (EPI distortion) is a type of geometric image distortion that may occur in both EPI and DWI images. EPI distortion is caused by inhomogeneity in the static field of the MRI scanner. The amount of EPI distortion may be different at different points of the EPI image, and the amount of distortion at each point may depend on the patient or subject being scanned.
FIG. 1(a) shows an image of a phantom (an object with known characteristics under MRI), where the image exhibits EPI distortion. In the image of FIG. 1(a), the phantom being imaged is an oil-based phantom having a shape resembling a flattened cylinder, roughly approximating the shape of a human torso. The grid of contrast lines that are visible in FIG. 1(a) are created by the MR hardware and are called saturation pulses. If there were no distortion, the contrast lines in the image would be parallel and perpendicular. In the image of FIG. 1(a), distortion is visible in the contrast lines. EPI images of different subjects may experience a different degree of distortion.
In addition to EPI distortion, DWI images may experience motion-probing gradient distortion (MPG distortion). MPG distortion is a type of geometric distortion that is caused by eddy currents that are induced by the MPG pulses in any conductive part of the scanner hardware, for example eddy currents that are induced in the gradient coils. MPG distortion is only present when MPG pulses are used. Therefore EPI images do not experience MPG distortion. The MPG distortion at each point in a DWI image may be a function of the position of that point in scanner equipment space (where scanner equipment space represents undistorted physical space, as opposed to the distorted space seen by the scanner before any correction). The amount of MPG distortion may not vary with different patients. However, the characteristics of MPG distortion may be specific to a particular scanner type, or specific to each individual scanner.
FIG. 1(b) shows an image of the phantom of FIG. 1(a) that exhibits both EPI and MPG distortion. In addition to the EPI distortion, the MPG distortion in the example of FIG. 1(b) results in a saddle-shaped distortion of the image.
A number of methods have been proposed for correcting EPI distortion. Most methods fall into two categories, field map methods and registration methods. Field map methods obtain EPI images with multiple echo times, and use the images to compute the amount of EPI distortion. Field map methods can be applied to correct EPI distortion in novel images. Given an set of images of the same anatomy with different echo times, it is possible to calculate the EPI distortion and correct all the images. However, field map methods may not apply to MPG distortion.
Registration methods align novel EPI images directly with a non-EPI reference image, for example T2W. T2W is chosen as a reference image because T2W images do not experience EPI or MPG distortion. Registration methods can correct for both MPG distortion and EPI distortion if they are robust enough to handle both EPI-T2W and DWI-T2W registration reliably. However, if either registration is inaccurate, then both types of distortion may be badly corrected.